The problem is here https://en.wikipedia.org/wiki/Sleeping_Beauty_problem
The solutions given for heads when waked are 1/2 or 1/3. I can easily understand 1/2 and I present my reasoning below. Is there a similar simple reasoning for 1/3?
As I understand it, a single trial is from Sunday to Wednesday. During this trial, either the beauty is woken once (if heads on Monday) or twice (if tails on Monday).
Let's suppose there are 4 trials, that means 4 coin tosses on Monday. Assuming a fair coin, 2 are heads, 2 are tails and the beauty wakes 4 times on Mondays.
For the 2 tails on Monday, the beauty has 2 more wakes on Tuesday. Assuming a fair coin again, 1 is heads, 1 is tails.
So in total, 4 trials, 6 wakings, 3 heads, 3 tails. So I get 1/2.
How does one get 1/3 using reasoning as simple as presented above?
